Ncert Exercises & Solutions

14.6 Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion?

(a) a = 0.7x

(b) $a = - 200 x^{2}$

(d) $a = 100 x^{3}$

For a simple harmonic motion:

$F = - kx \Rightarrow ma = - kx$
$\Rightarrow a = - \frac{k}{m} x$

Among the given equations, only equation a = –10 x is written in the above form with $\frac{k}{m} = 10$
Hence, this relation represents SHM.